Improving the Stability of Predictor-Corrector Methods by Residue Smoothing

Residue smoothing is usually applied in order to acceleratethe convergence of iteration processes. Here, we show that residuesmoothing can also be used in order to increase the stabilityregion of predictor-corrector methods. We shall concentrateon increasing the real stability boundary. The iteration parametersand the smoothing operators are chosen such that the stabilityboundary becomes as large as c(m, q)m²4^g where m is the numberof right-hand side evaluations per step, q the number of smoothingoperations applied to each right-hand side evaluation, and c(m,q) a slowly varying function of m and q, of magnitude 1.3 ina typical case. Numerical results show that, for a variety oflinear and nonlinear parabolic equations in one and two spatialdimensions, these smoothed predictor-corrector methods are atleast competitive with conventional implicit methods.     

Maintenance optimization on parallel production units

The optimal preventive-maintenance schedule for a productionsystem consisting of N identical parallel production units isinvestigated. The lifetimes of the units are IFR-distributed,i.e. with an increasing failure rate, and are supposed to bestatistically independent. The relevant costs are due to productionlosses, which are increasing and convex in the number of unitsthat are out of operation simultaneously. Actual maintenancecosts (either preventive or corrective) are supposed to be negligibleas compared to the costs due to these production losses. First we consider the apparently trivial case of geometric (discrete-time)or exponential (continuous-time) lifetime distributions forthe units. In this situation, preventive maintenance cannotimprove the condition of a unit. Hence, apparently the onlyrelevant policy is to do corrective maintenance on failed units.However, the analysis reveals that this conclusion is not correct.It turns out that taking non-failed units out of operation deliberatelycan be better than restricting to corrective maintenance only. We first show that, in the case of geometrically distributedlifetimes and unit repair times, the optimal preventive–maintenancepolicy is characterized by a single control limit K. Wheneverthe number of working units is less than or equal to K, no unitsare taken out of operation, while i – K units are setapart whenever i ( > K) units are operational. Next we consider the case with exponentially distributed lifetimesand repair times. Moreover, we assume that the repair capacityis limited, in the sense that only s ( N) units can be underrepair simultaneously. We show that, also in this case, it canbe optimal to take a working unit out of operation until thenext decision epoch (which is either a failure epoch or a repaircompletion epoch). It is shown that the optimal policy has aweak monotonicity property: the number of units which remainin operation increases with the number of available units. However,it is not necessarily true that, under the optimal policy, thenumber of units in standby position increases with the numberof available units. Numerical examples are presented which illustrate that, fora wide range of parameter values, the easiest policy (only performcorrective maintenance on failed units) performs rather wellas compared to the overall optimal policy. Finally we consider the possible extension to the practicallymore interesting case of non-exponential lifetime distributions.In particular, we assume that the lifetimes are composed oftwo non-identical exponential phases. A unit in its first lifephaseis called ‘good’, while a unit in its second phaseis called "doubtful". In this situation, one has the optionto put a good or doubtful unit in standby position until thenext decision epoch or to perform preventive maintenance ona doubtful unit. The latter brings a unit back from the doubtfulinto the good state. An indication is given of the problemsthat arise in generalizing the results obtained for the exponentialcase.     

A procedure of determining potential energy surfaces of triatomic molecules from inversion of spectroscopic data

In this paper,we have suggested an iterative procedure of optimization of the linearparameters in an analytic potential energy function for a triatomic molecule,by combining both variational and second order perturbation methods.The most important feature of this procedure is that the objective function is an analytical expression which can be optimized easily.The application to the water molecule is presented.     

EFFECTS OF UV-B IRRADIATION ON SOROCARP DEVELOPMENT OF Dictyostelium discoideum

Abstract— The effect of UV-B irradiation on the development of Dictyostelium discoideum from amoebae to mature sorocarps was studied. Radiation with wavelength ≤ 310 nm was very efficient in retarding and inhibiting the development especially when the organisms were exposed during the first 12 h. At a wavelength of 280 nm an irradiation of 1 h at an irradiance of < 0.2 W m^-2 was sufficient to completely inhibit sorocarp development. The fluence-dependence shows as well that the development of D. discoideum is a very sensitive system to indicate UV-B irradiation. Furthermore, since the sorocarp development is concluded within 48 h it can serve as a fast bioassay for hazardous levels of increased UV-B irradiation which have been predicted as a result of the ozone reduction in the stratosphere due to the manmade production and emission of chlorofluoromethanes.     

AN IMPLICIT SURFACE TENSION ALGORITHM FOR PICARD SOLVERS OF SURFACE–TENSION–DOMINATED FREE AND MOVING BOUNDARY PROBLEMS

One of the methods for solving a free or moving boundary problem is the use of Picard solvers which solve the geometry and the velocity field successively. When, however, the kinematic condition is used for updating the geometry in this technique, numerical stability problems occur for surface-tension-dominated flow. These problems are shown here to originate from the unstable integration of the local smoothing of the surface by surface tension. By an extension of the surface tension contribution to the flow field an implicit treatment of surface tension is obtained which overcomes these stability problems. The algorithm is applicable to both free and moving boundary problems, as will be shown by examples in this paper.     

Nonlinear Instability of the Two-Dimensional Striation Model About Smooth Steady States

The two-dimensional striation model consists of a nonlinear system of PDE's which arises in the modeling of the ionospheric plasma. The local-in-time existence of strong solutions is first proved using Banach's fixed point theorem. Then, under physically relevant assumptions, the system is shown to be nonlinearly unstable as soon as it is linearly unstable. Moreover, the instability occurs before the possible blow-up time of the solution. The proof relies on an earlier work of Hwang and Guo (2003 Hwang , H. J. , Guo , Y. ( 2003 ). On the dynamical Rayleigh–Taylor instability . Arch. of Rat. Mech. Anal. 167 : 235 – 253 .[Crossref], [Web of Science ®] , [Google Scholar]). The first step of the proof is to investigate under which conditions the linearized system is unstable and to prove that its spectrum is bounded, by means of a variational formulation. The second one consists in constructing a family of solutions depending on the parameter δ measuring the smallness of the perturbation to the steady-state. Thanks to the boundedness of the linearized spectrum, this family of solutions is shown to be unstable by means of a power series expansion in δ.     

Application of a Direct Stiffness Method to Wave Propagation in Multiphase Poroelastic Media

In this paper, it is demonstrated how a direct stiffness method for wavepropagation in multilayered saturated poroelastic media, based on integraltransform techniques, can be modified to account for a small amount of gasin the pores. Unsaturated media with small gas fractions can be treatedusing Smeulders extension of Biots poroelastic theory. The effect of thepresence of gas bubbles on the fluid bulk modulus and the dispersioncharacteristics of a water-saturated sand of Mol is demonstrated. Thedirect stiffness method is illustrated with a numerical example wheretransient wave propagation in a dry, saturated and unsaturated halfspaceis considered.